Journal of the
Korean Mathematical Society JKMS

Relationships between the Ricci curvature and the squared mean curvature and between the shape operator associated with the mean curvature vector and the sectional curvature function for slant submanifolds of an $S$-space-form are proved, particularizing them to invariant and anti-invariant submanifolds tangent to the structure vector fields.

Keywords: $S$-space-form, slant immersion, mean curvature vector, Ricci curvature, shape operator

MSC numbers: 53C25, 53C40